The fact that Ériu is represented as goddess of Ireland, she is often interpreted as a modern day personification of Ireland, although since the name "Ériu" is the older Irish form of the word Ireland, her modern name is often modified to "Éire" or "Erin" to suit a modern form.
With her sisters, Banba and Fódla, she was part of an important triumvirate of goddesses. When the Milesians arrived from Galicia each of the three sisters asked that her name be given to the country. This was granted to them, although Ériu (Éire) became the chief name in use (Banba and Fódla are still sometimes used as poetic names for Ireland, much as Albion is for Great Britain).
Ériu, Banba and Fódla are interpreted as goddesses of sovereignty.
According to Seathrún Céitinn the three goddesses of Éire, Banbha and Fódla were Badhbh, Macha and Móirríoghan (respectively?). Like Ériu, Badhbh is also sometimes named as a daughter of Ernmas; the two goddesses may possibly therefore be seen as equivalent.
Different texts have attributed different personal relationships to Ériu. Her husband has been named as Mac Gréine (‘Son of the Sun’). She has also been portrayed as the lover of Elatha, a prince of the Fomorians, with whom she had a son Bres, and as the mistress of the hero Lugh.
The University of Wales' reconstructed Proto-Celtic lexicon gives *Φīwerjon- (nominative singular Φīwerjō) as the Proto-Celtic etymology of this name. This Celtic form implies Proto-Indo-European*piHwerjon-, likely related to the adjectival stem *piHwer- "fat" (cf. Sanskritpīvan, f. pīvarī and by-form pīvara, "fat, full, abounding") hence meaning "fat land" or "land of abundance", applied at an early date to the island of Ireland. The Proto-Celtic form became *īweriū in Q-Celtic (Proto-Goidelic). From a similar or somewhat later form were also borrowed Greek ἸέρνηI[w]ernē and ἸουερνίαIouernia; the latter form was converted into LatinHibernia.
Boydell, Barra. "The female harp: The Irish harp in 18th- and early–19th-century Romantic nationalism", RIdIM/RCMI newsletter XX/1 (spring 1995), 10–17.